text: Stokess wave theory, when using a low order of the perturbation expansion (e.g. up to second, third or fifth order), is valid for nonlinear waves on intermediate and deep water, that is for wavelengths (λ) not large as compared with the mean depth (h'). In shallow water, the low-order Stokes expansion breaks down (gives unrealistic results) for appreciable wave amplitude (as compared to the depth). Then, Boussinesq approximations are more appropriate. Further approximations on Boussinesq-type (multi-directional) wave equations lead – for one-way wave propagation – to the Korteweg–de Vries equation or the Benjamin–Bona–Mahony equation. Like (near) exact Stokes-wave solutions, these two equations have solitary wave (soliton) solutions, besides periodic-wave solutions known as cnoidal waves.